Analysis of Thermal Effects in a Cavitating Inducer Using Rayleigh Equation

Jean-Pierre Franc,Christian Pellone

doi:10.1115/1.2746919

Abstract

AbstractA simple model based on the resolution of Rayleigh equation is used to analyze thermal effects in cavitation. Two different assumptions are considered for the modeling of heat transfer toward the liquid∕vapor interface. One is based upon a convective type approach using a convection heat transfer coefficient or the equivalent Nusselt number. The other one is based upon the resolution of the heat diffusion equation in the liquid surrounding the bubble. This conductive-type approach requires one to specify the eddy thermal diffusivity or the equivalent Peclet number. Both models are applied to a cavitating inducer. The basic pressure distribution on the blades is determined from a potential flow computation in a two-dimensional cascade of flat plates. The sheet cavity, which develops from the leading edge, is approximated by the envelope of a hemispherical bubble traveling on the suction side of the blade. Cavity shape and temperature distribution predicted by both models are compared. The evolutions of cavity length with the cavitation number for cold water (without thermal effects) and for Refrigerant 114 at two different temperatures is compared to experimental data. Such a simple model is easy to apply and appears to be quite pertinent for the analysis of thermal effects in a cavitating inducer.

Highlights

In a number of fluids, the development of cavitation goes with significant thermal effects
It is of major concern to observe that, in such models based on a well-defined interface between the liquid and either a cavitation bubble or a sheet cavity, heat transfer by conduction characterized by the classical liquid thermal diffusivity ␣ᐉ is far too small to account for the measured values of the temperature drop
To account for thermal effects, it is necessary to consider in Rayleigh equation the vapor pressure corresponding to the actual temperature Tc inside the bubble, which is different from the liquid temperature

Summary

Introduction

In a number of fluids, the development of cavitation goes with significant thermal effects. It is of major concern to observe that, in such models based on a well-defined interface between the liquid and either a cavitation bubble or a sheet cavity, heat transfer by conduction characterized. Thermal effects are essentially regulated by the limited volume of liquid able to supply the heat for vaporization and not by heat diffusion as for interface models. The present paper is devoted to an analysis of thermal effects on the basis of the Rayleigh equation It belongs to the class of interface models for which heat transfer through the thermal boundary layer is supposed to be the limiting physical phenomenon. The sheet cavity observed experimentally is compared to the computed envelope of a hemispherical bubble, which grows and collapses on the suction side of the blades This kind of simple model obviously suffers from limitations. The present work supplies a theoretical support for the physical interpretation and understanding of experimental results

Pressure Distribution Computation

Basic Equations

Results and Discussion

Concluding Remarks